This paper proposes the study of a new computation model that attempts to address the underlying sources of performance degradation (e.g. latency, overhead, and starvation) and the difficulties of programmer productivity (e.g. explicit locality management and scheduling, performance tuning, fragmented memory, and synchronous global barriers) to dramatically enhance the broad effectiveness of parallel processing for high end computing. In this paper, we present the progress of our research on a parallel programming and execution model - mainly, ParalleX. We describe the functional elements of ParalleX, one such model being explored as part of this project. We also report our progress on the development and study of a subset of ParalleX - the LITL-X at University of Delaware. We then present a novel architecture model - Gilgamesh II - as a ParalleX processing architecture. A design point study of Gilgamesh II and the architecture concept strategy are presented.